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thanks

I never asked a question. But from what I've seen on this website (I've dugged through a lot of posts out of interest):

It depends on:
(1) Who is online

(2) The difficulty of the question

(3) The reputation of the question asker

(4) The legitimacy of the question.

Cphill, EP, and Cal tend to answer the question as soon as possible. While other answerers (like Melody, Heureka, and Alan) usually look for harder problems that may interest them. They also tend to come online a little less. The question difficulty is determines a lot too. College level math or competition math (especially olympiad level) take the longest. Intermediate to basic level competition math take some time. The fastest are easy competition problems to school level problems. The reputation of the question asker may motivate some to answer the question. Question's posted by Melody or CPhill gain attention, while Guest questions are the lowest priority. The question needs to be legit. Questions like long chains of homework usually takes a long time. A single simply formatted question takes less time.

Hint: The angle formed by a tangent line and the circle's radius when is a 90 degree angle

Using this info, can you find the slope?

Another hint: The slopes of perpendicular lines are negative reciprocals of each other.

Example of a negative reciprocal:

\(2\) and \(-\frac{1}{2}\) 

Slope from center to point     5-2  /  5-3   =  3/2      perpindicular slope  =  -1 / 3/2  = - 2/3

Well, I tend to post my questions when a lot of users are online. So around 5 minutes...

Take a look at EP's answer here:

Linear    so  y = mx+ b     m is given as -2.2

                    y = -2.2 x + b     when x = 3.5     y = 5.1    sub that in

                   5.1 = -2.2 (3.5)  + b         so b = 12.8  

y = -2.2 x   + 12.8        now put in x = 6.9    to find the value of  'y'   

x = 6% amount      interest in one year  = .06 x

(50000-x) = 12% amount    interest after one year = .12(50 000 - x)       summed = 3600

.06x       +      .12(50 000 -x)         = 3600      solve for 'x'   the 6% amount, then 12% amount = 50 000 - x

You use variables. 

x/2=45-20

x/2=25

x/2*2=25*2

x=50

I got confused if order mattered, but thank you!

The number of orderings is 8*6*4*2 = 384.

By calculus,

\[[\mathcal{R}_1] = 30 + \frac{1}{4} \cdot \pi \cdot 10^2 + \int_0^5 \sqrt{100 - x^2} \ dx + \int_0^6 \sqrt{100 - x^2} \ dx.\]

We can write out the areas similarly, to get [R_1] - [R_2] - [R_3] + [R_4] = 80.

So I had the answer all along but I got it wrong because I didnt put a negative. But it was as simple as I thought. -.45       5/11 

I answered -.04 but that wasnt correct. Remember the slope is downward.

I posted an answer about this same question here:

The slope will be 5inches/11ft

In inches, the slope will be 5/132 or about 0.04.

Is this correct? If not, I will try again!

thanks but it doesnt answer part c. 

  I think it is a little too much detail...and too time consuming..   You are good to give explanations rather than just answers as so many do.  I tend to believe that they should have the  knowledge of how to solve any problem they posted and know the basics of how to solve it given a little nudge/explanation in the right direction.  I tend to give some direction and try to avoid giving a final answer, but let them do some of the calculations....o/w they will just run with the answer and not try to do anyhting themselves and not learn anything.  I believe, given the number of repeated questions, a lot of the Q's are from homeschooled folks......they have to put something in the box on the computer screen to 'advance' or get the homework done and that becomes their objective:   Fill in the box and move on....they may get 'advanced' or promoted, but then they are in over their heads at a level above their skills and more questions will be posted 'looking for answers' .....        YMMV         

the answer was .49. 1.06^1/12=1.004867551-1=.0048675506x100=.4867550565 rounds to .49.  thanks anyway!